The diagonal of a rectangle is 37. The length is 1 less than the width. How do I find the perimeter?

i know that i use the pythagorean theorem x^2 + (3x-1)^2 = 37 but i dont know how to solve that or:i know that i use the pythagorean theorem x^2 + (3x

i know that i use the pythagorean theorem x^2 + (3x-1)^2 = 37 but i don't know how to solve that

or:i know that i use the pythagorean theorem x^2 + (3x-1)^2 = 37 but i don't know how to solve that

or:Let the width be (x) units... Therefore, the length will be (3x-1) unitsDiagonal^2 = (Side1)^2 + (Side2)^2therefore, (37)^2 = (x)^2 + (3x-1)^2therefore, 1369 = x^2 + 9x^2 - 6x + 1therefore, 1369 = 10x^2 - 6x + 1therefore, 10x^2 - 6x - 1368 = 0therefore, 5x^2 -3 x - 684 = 0 ... dividing by 2therefore, 5x^2 - 60x + 57x - 684 = 0 ... splitting the middle termtherefore, 5x(x - 12) + 57(x - 12) = 0therefore, (x - 12) (5x + 57) = 0Therefore, either x - 12 = 0 OR, 5x + 57 = 0 ... If ab=0 then either a=0 or b=0Therefore, x = 12 OR x = -57/5But Length cant be negative... Therefore, x = -57/5 is discardedtherefore x = 12so, width is 12 and length is (x - 1) = 11perimeter of rectangle = 2(length + width) ... formulatherefore, perimeter = 2(12 + 11)therefore, perimeter = 2 * 23therefore, perimeter = 46 uintsPlz comment of this

or:At first I was a bit puzzled when I saw this peculiar (3x - 1)\u00b2. Well, the solution, a:= width = 12 and hence, as b equals a -1, b:= length = 11, is wrong. Go test it:sqrt(11\u00b2 + 12\u00b2) = 37??? Nope, is just 16.2788something. So, the condition is not fulfilled.As the length, b, equals width a - 1, we can express b in terms of a, which we shall do henceforth throughout this calculation. Get yourself a cup of tea and lo and behold:Pythagoras tells us that a\u00b2 + (a-1)\u00b2 = 37\u00b2(a-1)\u00b2 is just (a-1)(a-1) = a\u00b2 - 2a + 1. Together with the width\u00b2 this sums up to:2a\u00b2 - 2a + 1 = 37\u00b2 = 13692a\u00b2 - 2a = 1368 | :2a\u00b2 - a = 684a\u00b2 - a - 684 = 0That's a simple quadratic equation, which can be solved. We get two solutionsone positive and one negative. We ignore the negative, as negative lengths of rectangles don't make much sense.a = 26.65817281...b = a - 1 = 25.65817......test it! Now the diameter of the rectangle has the demanded length of 37.sqrt = square rootsqrt(a\u00b2 + b\u00b2) = 37That's it.

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